This assignment is also implemented with Common Lisp. However, the matrix library, lisplab, is no longer used because it doesn’t have the SVD and other convenient functions. Instead the matlisp is used for computing matrix operations.

Improving the corner position picked manually is done by Harris Corner Detector. First, for each image (view1.png and view2.png) the derivative of gaussian image(DoG) is required. Applying the Sobel filter and Gaussian filter to the images for each color components makes the DoG images. Depending the direction of Sobel filter, the images has the direction dx or dy. The result image is saved in img1_dx.png, img1_dy.png, img2_dx.png, img2_dy.png.

After that the auto-correlation matrix is computed by applying the gaussian filter which is the same size with the patch. By performing SVD to the structure tensor, the lambda x and y are returned. The Harris Corner Detector equation

R = ld-x * ld-y - 0.06*(ld-x + ld-y)^2

is calculated to determine whether the point has corner or not.

The matrix A (Nx9) is made by the corner points. In order to solve the linear equation at least four correspondence is required. After constructing the matrix applied SVD to A and V’ * [0 0 0 0 0 0 0 0 1]’ is the homography matrix.

I implemented the user interface with SDL library and OpenGL to pick the correspondence points on the images. The homography matrix is 2D projective matrix, but I need 3D projective matrix because OpenGL only supports 3D matrix.

The following matrix conversion is implemented in “2D->3D-transform” function.

H = |a b c|

H’ = |a b 0 c|

The coordinate for picking point is same with OpenGL’s default coordinate whose the origin is lower left.

Computing the topview image is done by performing another homography for the square shape of floor tiles in the composited image.